Chapter2 - Chapter Two The Time Value of Money MGMT 109...

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1 Chapter Two The Time Value of Money MGMT 109 Managerial Finance Professor Lu Zheng Preview of Chapter Two Preview of Chapter Two FV of a single cash flow PV of a single cash flow FV and PV of a stream of cash flows The general case Special cases Annuity Perpetuity Constant Growth Perpetuities Constant Growth Annuities Using the time line – example Compounding (EAR vs. APR)
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2 Explaining Interest In a speech delivered before the Yale Socialist Club a decade after his return to New Haven, Irving Fisher related this minor incident to his stay in Santa Barbara: Discovering that the man who came to massage him was a Socialist and believed that "interest is the basis of capitalism and is robbery," my father determined to make the most of his pedagogical opportunity. To the question "How much do I owe you?" the masseur replied, "Thirty Dollars." "Very well. I will give you a note payable a hundred years hence. I suppose you have no objection to taking this note without interest. At the end of that time you, or perhaps your grandchildren, can redeem it." "But I cannot afford to wait that long." "I thought you said that interest was robbery. If interest is robbery, you ought to be willing to wait indefinitely for the money. If you were willing to wait ten years, how much would you require?" "Well, I would have to get more than thirty dollars." With a gleam of triumph, Father thrust home. "That is interest." [Irving Norton Fisher, My Father Irving Fisher (New York: Comet, 1956), p.77] The Idea of Interest We may never know when finance began, because financial contracts are as old as written language—in fact, writing appears to have been invented for the purposes of recording financial deals. The first archaeological traces of financial activity appear in the earliest urban civilizations in the Near east. What gave the ancient Sumerians the idea of charging each other interest? Linguistic evidence provides a clue. In the Sumerian language, the word for interest, mash, was also the term for calves. In ancient Greek, the word for interest, tokos, also refers to the offspring of cattle. The Latin term pecus, or flock, is the root of our word “pecuniary.” The Egyptian word for interest, ms, means “to give birth.” All these terms point to the derivation of interest rates as the natural multiplication of livestock. [Financing Civilization, by William Goetzmann] The Time Value of Money Why is time = money? Positive interest rates/returns. The time value of money is critical for the comparison of cash flows with different timing (e.g., project evaluation, security valuation).
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3 Consider the time line above: PV is the Present Value, that is, the value today. FV is the Future Value, or the value at a future date.
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Chapter2 - Chapter Two The Time Value of Money MGMT 109...

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